Difference between revisions of "User:Herb"

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* [[Dispersion Assumptions]]
 
* [[Dispersion Assumptions]]
 
* [[Measuring Precision]]
 
* [[Measuring Precision]]
* References
+
* [[Herb_References]]
 
* Examples
 
* Examples
  

Revision as of 19:00, 6 June 2015

Dispersion Assumptions

MediaWiki:Sidebar

My notion of sidebar:



Measurements

Extreme Spread

Figure of Merit

Mean Radius


Sighting a Weapon

Derivation of the Rayleigh Distribution Equation

Fliers vs. Outliers

--- Carnac the Magnificent


sighting shot distribution

The Mean Radius is the average distance over all shots to the groups center.

Given
  • set of n shots {\( (h_1, v_1), (h_2, v_2), ..., (h_n, v_n) \)}
    for which all of the (h,v) positions are known
Assumptions
  • Origin at \((r,\theta) = (0,0)\)
  • Rayleigh Distribution for Shots
    • \(\sigma_h = \sigma_v\)
    • \(\rho = 0\)
    • \(PDF_{r_i}(r) = \frac{r}{\sigma^2}e^{-r^2/2\sigma^2}\)
  • With conversion from Cartesian coordinates to Polar coordinates, \(\theta\) will be entirely random and independent of radius
  • No Flyers
Data Pretreatment Shot impact positions converted from Cartesian Coordinates (h, v) to Polar Coordinates \((r,\theta)\)
  • Origin translated from Cartesian Coordinate (\(\bar{h}, \bar{v}\)) to Polar Coordinate \((r = 0, \theta = 0)\)
Experimental Measure \(\bar{r_n}\) - the average radius of n shots

\(\bar{r_n} = \sum_{i=1}^n r_i / n\)
    where \(r_i = \sqrt{(h_i - \bar{h})^2 + (v_i - \bar{v})^2}\)

\(PDF_{r_0}(r; n, \sigma)\) \(\frac{nr}{\sigma^2}e^{-nr^2/2\sigma^2}\)
\(CDF_{r_0}(r; n, \sigma)\) \(1 - e^{-nr^2/2\sigma^2}\)
Mode of PDF(\(\bar{r_n}\)) \( \frac{\sigma}{\sqrt{n}}\)
Median of PDF(\(\bar{r_n}\)) \( \frac{\sigma}{\sqrt{n}}\sqrt{ln{(4)}}\)
Mean of PDF(\(\bar{r_n}\)) \( \frac{\sigma}{\sqrt{n}}\sqrt{\frac{\pi}{2}}\)
(h,v) for all points? Yes
Symmetric about Measure?
NSPG Invariant No
Robust No

master ref page

I like the structure of this wiki page. You can look at the "groups of papers" then jump to a specific paper and use the browser back button to go back to the group.

Could we make this the "master" reference page?

(1) Move references to top of page (2) put TOC that floats to right (3) Have level 1 headings for various topics (eg CEP Literature, EEP Literature, ES, Rayleigh Model, Hoyt Model) (4) Each level 1 heading would have various "groups" of papers. (5) From some paper that we want to discuss create an off page link for that paper. (eg comments on "prior Art" page

how I'd redo references so as to provide some that was "linkable" and could be "named"

So Blischke_Halpin_1966 could be name of wiki page and a "named" link within the page. thus reference in a wiki page would be something like:

: yada yada yada (Blischke_Halpin_1966) yada yada yada 

the link would jump to the "master" page of references to that entry.

Blischke_Halpin_1966
Blischke, W. R., & Halpin, A. H. (1966). Asymptotic properties of some estimators of quantiles of circular error. Journal of the American Statistical Association, 61 (315), 618-632. http://www.jstor.org/stable/2282775
Chew_Boyce_1962
Chew, V., & Boyce, R. (1962). Distribution of radial error in bivariate elliptical normal distributions. Technometrics, 4 (1), 138–140. http://www.jstor.org/stable/1266181
Culpepper_1978
Culpepper, G. A. (1978). Statistical analysis of radial error in two dimensions (Tech. Rep.). White Sands Missile Range, NM
U.S. Army Material Test and Evaluation Directorate. http://handle.dtic.mil/100.2/ADA059117